This question is from the National University of Colombia entrance exam in 2006 (translated from Spanish).

The function y=4cos(x/2) - 3sin2x is of period:

A. π
B, 4π
C. 3π
D. 2π

I learned to divide the period of cos by 2π, so 2π/1/2 would be 4π I thought, and the period for the sin would be 2π/2 is π, and the least common number to divide into seems like it would make the answer 4π, but the answer sheet says D, 2π, and I can't figure out why. I have their entrance exam in two days and I need to understand all this. Please help me. Thank you

May 6th 2009, 06:20 PM

pickslides

The answer is B as this is the biggest period of 4cos(x/2) and 3sin2x

In short find the individual period of both trig functions you are summing, the period of the summed functions will be the bigger of the 2.